Question

Which of the following statements are true concerning sign conventions for image formation?

Check all that apply.

	A virtual image has a positive image distance; a real image has a negative image distance.
	For an upright image, the magnification is positive; for an inverted image, the magnification is negative.
	When the center of curvature of a spherical mirror is on the same side as the reflected light, the radius of curvature is positive; otherwise, it is negative.
	A converging lens has a negative focal length; a diverging lens has a positive focal length.
	When the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive; otherwise, it is negative.

Answer 1

Concepts and reason

The concepts used to solve this problem are sign conventions for image formation.

Use the sign rule for the object distance and sign rule for the radius of curvature in the case of reflection at a spherical surface to find the correct option.

Fundamentals

The sign rule for the object distance is defined as the when the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive; otherwise, it is negative.

The sign rule for the radius of curvature in the case of reflection at a state that when the center of curvature of a spherical mirror is on the same side as the reflected light, the radius of curvature is positive; otherwise, it is negative.

For an upright image, the magnification is positive and for an inverted image the magnification is negative.

The sign convention for the lenses and mirrors are similar.

From the rule of sign convention of image formation if the image is far side of the lens, the image distance is positive and the image is real.

If the image and the object are on the same side, the image distance is negative and the image is virtual.

For converging lens the focal length is positive and for a diverging lens focal length is negative.

The given below are the incorrect options for image formation.

• A virtual image has a positive image distance and a real image has a negative image distance.

• A converging lens has a negative focal length and a diverging lens has a positive focal length.

From the sign rules, for the radius of curvature of a spherical surface, when the center of curvature is on the same side as the outgoing light, the radius of curvature is positive; otherwise, it is negative.

From the sign rules for the object distance, when the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive. Otherwise it is negative.

Hence, the given option that when the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive; otherwise, it is negative is correct.

As per the sign rule, for an upright image the magnification is positive; for an inverted image, the magnification is negative.

Hence, the given option that for an upright image the magnification is positive; for an inverted image, the magnification is negative is correct.

Ans:

When the center of curvature of a spherical mirror is on the same side as the reflected light, the radius of curvature is positive; otherwise, it is negative.

When the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive; otherwise, it is negative.

For an upright image, the magnification is positive; for an inverted image, the magnification is negative.